Question

You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. Implement the test at the 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table)

a. Select the null and the alternative hypotheses.

• H₀: p = 0.70; H_A: p ≠ 0.70

• H₀: p ≤ 0.70; H_A: p > 0.70

• H₀: p ≥ 0.70; H_A: p < 0.70

b. Calculate the sample proportion. (Round your answer to 3 decimal places.)

c. Calculate the value of test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

Solution :

a ) This is the two tailed test .

The null and alternative hypothesis is

H₀ : p =0.70

H_a : p 0.70

x = 62

n = 80

b ) = x / n = 62 / 80 = 0.775

P₀ = 0.70

1 - P₀ = 1 - 0.70 = 0.30

c ) Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.775 - 0.70 / [0.70 - 0.30 /80 ]

= 1.464

Test statistic = z = 1.46

P-value = 0.1432

= 0.01

P-value ≥

0.1432 ≥ 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that